Cheesy Dutch Baby With Green Sauce

Name: Cheesy Dutch Baby With Green Sauce
Ingredients: 1¼ cups all-purpose flour; 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, divided; Freshly ground black pepper; 5 large eggs, room temperature; 1¼ cups milk, room temperature; 4 Tbsp. unsalted butter; 6 oz. sharp cheddar, coarsely grated; 1 oz. Parmesan, finely grated; 1 garlic clove, finely grated; 2 cups (packed) mixed tender herbs (such as parsley, cilantro, mint, and/or chives); 3 Tbsp. extra-virgin olive oil; 3 Tbsp. fresh lemon juice; 3 cups trimmed arugula